erweitern (x^2-2)/(x^6-8)

Lösung

erweitern

\frac{x ^{2} - 2}{x ^{6} - 8}

\frac{1}{x ^{4} + 2 x ^{2} + 4}

Schritte zur Lösung

\frac{x ^{2} - 2}{x ^{6} - 8}

Faktorisiere

x^{2} - 2 : (x + 2) (x - 2)

= \frac{( x + 2 ) ( x - 2 )}{x ^{6} - 8}

Faktorisiere

x^{6} - 8 : (x + 2) (x - 2) (x^{4} + 2 x^{2} + 4)

= \frac{( x + 2 ) ( x - 2 )}{( x + 2 ) ( x - 2 ) ( x ^{4} + 2 x ^{2} + 4 )}

Streiche

\frac{( x + 2 ) ( x - 2 )}{( x + 2 ) ( x - 2 ) ( x ^{4} + 2 x ^{2} + 4 )} : \frac{1}{x ^{4} + 2 x ^{2} + 4}

= \frac{1}{x ^{4} + 2 x ^{2} + 4}

e x p an d x^{4} + 4 x + 9 (x^{3} + 1) d x

e x p an d (2 + π)^{2}

e x p an d (X - 1) (e^{X} - e)

e x p an d \frac{3 e ^{- 3 s}}{s ( s ^{2} + 1 )}

e x p an d \frac{n ( n + 1 ) + 1}{x ^{2}}